Abstract
In this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.
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Supported by the National Natural Science Foundation of China (11771178), the Science and Technology Development Program of Jilin Province (20170101152JC), the Science and Technology Program of Jilin Educational Department during the “13th Five-Year” Plan Period (JJKH20200951KJ) and Fundamental Research Funds for the Central Universities.
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Liu, W., Zhang, Y. Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation. Appl. Math. J. Chin. Univ. 36, 243–255 (2021). https://doi.org/10.1007/s11766-021-3882-7
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DOI: https://doi.org/10.1007/s11766-021-3882-7